Dynamic Pricing under a Static Calendar.

This work is motivated by our collaboration with a large Consumer Packaged Goods (CPG) company. We have found that while they appreciate the advantages of dynamic pricing, they deem it operationally much easier to plan out a static price calendar in advance. In this paper, we investigate the efficacy of static control policies for dynamic revenue managementproblems. In these problems, a firm has limited inventory to sell over a finite time horizon where demand is known but stochastic. We consider both pricing and assortmentcontrols, and derive simple static policies in the form of a price calendar or a planned sequence of assortments, respectively. We show that our policies are within 1-1/e (approximately 0.63) of the optimum under stationary (IID) demand, and 1/2 of optimum under non-stationary demand, with both guarantees approaching 1 if the starting inventory is large. A main contribution of this work is developing a system of tools for establishing best-possible performance guarantees relative to linear programming relaxations: in the stationary setting, structural properties about static policies which provide a complete characterization of tight bounds; and in the non- stationary setting, an adaptation of the prophet inequalities from optimal stoppingtheory to pricing and assortmentproblems. Finally, we demonstrate on data from the CPG company that our simple price calendars are effective.